Monte Carlo simulations of a solenoid spectrometer for ... · (Courtesy J. Erler) Project P2 @...
Transcript of Monte Carlo simulations of a solenoid spectrometer for ... · (Courtesy J. Erler) Project P2 @...
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D. Becker, K. Gerz, T. Jennewein,S. Baunack, K. S. Kumar, F. E. Maas
Institute for Nuclear Physics,JGU Mainz
IEB-Workshop, June 17-19 2015, Ithaca, NY, USA
Monte Carlo simulations of a solenoid spectrometer
for Project P2
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Outline
● Project P2 @ MESA:A new high precision determination of the electroweak mixing angle at low momentum transfer
● P2 main dector concept:Monte Carlo simulations of a solenoid spectrometer
● Monte Carlo simulations regardinga precision measurement of the weak mixing angle at higher beam energies and beam current
Highest probability
Monte Carlo is all about probability...
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(Courtesy J. Erler)
Project P2 @ MESA:
● New high precision determination of the proton weak charge Q
W(p)
at low Q² ~ 6·10-3 GeV²/c²
● Precision goal:ΔQ
W(p) = 1.9 %
Δsin2θW = 0.15 %
● Measurement of QW(p)
through parity violation in elastic e-p scattering
The global situation
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● QW(p): Proton weak charge,
QW(p) = 1-4·sin2(θ
W)
(tree level)
● F(Q2): Nucleon structure contribution, small
at low Q²
totalQW
(p)e.m.
axial
strangeness
● Beam energy = 150 MeV● Detector acceptance = 20 deg
e
eP
e'
Detector
s
s
p
h=s⃗⋅p⃗|⃗s⋅p⃗|
=±1Parity violating asymmetry in elastic e-p scattering:
A PV∼sin2
θW
A PV=
−G FQ2
4 √2π α[QW ( p)−F (Q2
)]
Access to the weak mixing angle
Parity violating asymmetry, averaged over solid angle
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Prediction of achievable precision and choice of kinematics
Δsin2(θW) = 3.2 · 10-4 (0.13 %) @
Beam energy: 150 MeVCentral scattering angle: 35 degDetector acceptance: 20 deg
γ-Z-box according to: Gorchtein, Horowitz, Ramsey-Musolf 1102.3910 [nucl-th]Form factor parametrizations: P. Larin and S, Baunack
● Monte Carlo approachto error propagationcalculation
● Assumption of back anglemeasurement of axial andstrange magnetic form factorin P2 → Reduction of form factor uncertainty by factor 4
● APV = -39.80 ppb ± 0.54 ppb (stat.) ± 0.34 ppb (other)
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The new M.E.S.A. facility in Mainz
Mainz Energy recovering Superconducting Accelerator:
● Normal-conducting injector LINAC
● Superconducting cavities in re-circulations
● Energy recovering mode: Unpolarized beam, 10 mA, 100 MeV, pseudo-internal gas-target, L ~ 1035cm-2s-1
● External beam mode: P = 85%±0,5%,150 µA, 155 MeV, L ~ 1039 cm-2s-1, <ΔA
app>
Δt= 0.1 ppb
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B = 0.6 T
e- beam,150 MeV
Quartz bars(Cherenkov)
Lead shieldingSuperconducting solenoid
60 cm liquid hydrogen target
PMTs
Unauthorizedhall access
(CAD-drawing by D. Rodriguez)
Experimental setup under investigation
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:OFF
Raytrace simulations in the magnetic field
Target
Solenoid
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.06 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.12 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.18 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.24 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.3 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.36 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.42 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.48 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.54 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.6 T
Raytrace simulations in the magnetic field
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.6 T
Raytrace simulations in the magnetic field
Shielding
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Beam energy = 155 MeVMoller, θ є [ 0°, 90°]Elastic e-p, θ є [25°, 45°]Elastic e-p, θ є [ 0°, 90°]
Magnetic field:0.6 T
Raytrace simulations in the magnetic field
Shielding
Quartz
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Geant4 Simulation of beam-target-interaction
Radial projection of spatial vertex distribution Energy deposition in target volume
● Coherent simulation of elastic e-p scattering for P2 is impossible with Geant4
● Sample initial state distribution forelastic e-p scattering→ To be used with event generator
● Use tree-level event generator forprimary event-generation
● Prototype of event generator withradiative corrections available and currently under evaluation
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Geant4 Simulation of detector module response
Tracking of optical photons in detector module
Create parametrization of photo electronyield for different
● Active materials
● Geometries
● Particle types
● Particle energies
● Impact angles
Photo electron yield distribution, E = 155 MeV
α/degβ/deg
p.e./cm
(K. Gerz)
(K. Gerz)
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e-p, θ in [25°, 45°]
E = 155 MeV I = 150 µA
e-p, θ not in [25°, 45°]
background● electrons● positrons● photons
Photo electron rate distribution Q² distribution of elastically scattered electrons
● Use initial state distribution with tree levelevent generator to simulate elastice-p scattering
● Tracking in realistic map of magnetic field,CAD-interface for definition of geometry
● Use parametrization of detector responseto predict distribution of photo electrons
● Use Q² distribution in error propagation calculation to predict the achievable precision in the weak mixing angle
Geant4 Simulation of experimental setup
e-p, θ in [25°, 45°]
A PV =−GFQ
2
4 √2π α[QW ( p)−F (Q2)]
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Facts and Figures
Beam energy 155 MeV
Beam current 150 µA
Polarization 85 % ± 0.425 %
Target 60 cm liquid hydrogen
Detector acceptance 2π·20° θ є [25°, 45°]
Detector rate 0.5 THz
Measurement time 1e4 h
<Q²> 4.49e-3 GeV²/c²
Aexp -28.35 ppb
The following results are based on error propagation calculations including the results of the Geant4 simulation of the experimental setup:
Total Statistics Polarization Apparative Form factors
Re(□γZA
)
Δsin2(θW) 3.1e-4
(0.13 %)2.6e-4
(0.11 %)9.7e-5
(0.04 %)7.0e-5
(0.03 %)1.4e-4
(0.04 %)6e-5
(0.03 %)
ΔAexp/ppb 0.44(1.5 %)
0.38(1.34 %)
0.14(0.49 %)
0.10(0.35 %)
0.11(0.38 %)
0.09(0.32 %)
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Achievable precision @ higher energies/beam current
Beam current: 1 mAPolarization: 85 % ± 0.425 %Target material: liquid hydrogenTarget: 60 cmMeasurement time: 10000 hDetector acceptance: 2π·20°ΔAapp: 0.1 ppb
total
Gp
M
Gp
E
Gp
A
γ-Z-box
counting statistics
beam systematics
total Gp
M
Gp
E
Gp
A
γ-Z-box
counting statistics
beam systematics
Δsin2θW
= 2.14 · 10-4 Δsin2θW
= 2.95 · 10-4
Beam energy: 300 MeVCentral scattering angle: 19°APV = (-30.8 ± 0.34) ppb<Q²> = 4.84e-3 GeV²/c²Rate elastic e-p: 1.8 THz
Beam energy: 500 MeVCentral scattering angle: 14°APV = (-24.8 ± 0.36) ppb<Q²> = 3.82e-3 GeV²/c²Rate elastic e-p: 3.6 THz
polarization polarization
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ShieldingTarget
Solenoid
Detector
A very first idea for 300 MeV
Moller, θ є [0°, 90°]Elastic e-p, θ є [9°, 29°]Elastic e-p, θ є [0°, 90°]
Beam energy: 300 MeVBeam current : 150 µACentral magnetic field: 1.8 Tesla
Rate predicition @ z = 3000 mm
Elastic e-p, θ in [9°, 29°]Elastic e-p, θ not in [9°, 29°]Moller, e-pMoller, backgroundPositrons, e-pPositrons, backgroundPhotons, e-pPhotons, background
detector
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ShieldingTarget
Solenoid
Detector
A very first idea for 500 MeV
Moller, θ є [0°, 90°]Elastic e-p, θ є [4°, 24°]Elastic e-p, θ є [0°, 90°]
Beam energy: 500 MeVBeam current: 150 µACentral magnetic field: 3 Tesla
Rate predicition @ z = 3000 mm
Elastic e-p, θ in [4°, 24°]Elastic e-p, θ not in [4°, 24°]Moller, e-pMoller, backgroundPositrons, e-pPositrons, backgroundPhotons, e-pPhotons, background
detector
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Summary
● Project P2 @ MESA:A new measurement of the weak mixing angle with precision goal: ΔQ
W(p) = 1.9 %
Δsin2θW = 0.15 %
● P2 main detector concept study:Solenoid spectrometer and 2π-Cherenkov-detector→ Δsin2θ
W = 0.13 %
● Measurement at higher beam energies and beam current:→ Very high precision in sin2θ
W at small scattering angles for 300 MeV
→ Most important contributions from gamma-Z-box and form factors→ Experiment may be difficult to perform with a solenoid because of small scattering angles→ Toroid may be better choice due to lower dependence on counting statistics
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BACKUP SLIDES
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Rtotal
ep=0.19 THz
⟨A PV⟩L ,ΔΩ=−39.8 ppb
Monte Carlo results:
Event rate distribution: Photo electron rate distribution:
I totalcathode
=1 µA
⟨A PV⟩L ,ΔΩ=−33.5 ppb
Monte Carlo results:
Include simulated response of detector modules
Use results of detector module simulation to transform eventrates into photo electron rates:
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Solenoid:● Full azimuthal coverage ● Compact setup● Superconducting coils
Weapon of choice: Solenoid or Toroid?
Toroid:● Loss of ~ 50 % azimuth
→ double measurement time● Larger setup● Copper coils
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We would like to use a superconducting solenoid...
A promising candidate: The FOPI solenoid (GSI, Darmstadt)
● Field strength: 0.6 T● Coil current: 725 A● Stored energy: 3.4 MJ● Material: Cu/Nb-Ti● Cable length: 22.5 km
● Inner diameter: 2.4 m● Total length: 3.8 m● Total weight: 108.7 tons● l-He consumption: 0.02 g/s, 0.6 l/h● l-N consumption: 3 g/s, 13 l/h (perm. cooling)
(Courtesy Y. Leifels)
Use fieldmap with Geant4 to simulate the P2 experiment
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E = 150 MeVI = 150 µAP = 0.85θ = 25° ± 10°L = 60 cmT = 10000 h
sin2(θW)
cou
nts
Aexp∼sin2
(θW )
sin2(θW )=Ζ(A exp , Aapp , E , P , L ,ΔΩ ,Re(□γZ) ,{f i})
Monte Carlo approach:
Sample distribution for sin2(θW) by assigning Gaussian distributions to each
parameter .ζ i∈{Aexp , Aapp , E , P , L ,ΔΩ, {f i}}
sin2(θW )+δsin2
(θW )=Ζ(ζi '+δζ i)
Set of form factor fit parameters
i i '
i
Extract Δsin2(θW) as
standard deviation.
N sampling-iterations yield sin2(θ
W)-distribution.
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Choice of new weighting function: Detection yield distribution
ϵ (z ,θ)≡ Rate of photo electrons in detector, produced in target at position z with angle θEvent rate according to Rosenbluth formula, produced in target at position z with angle θ
Ideal case Simulation result
Target dθ
Detector
dz
⟨APV⟩L, ΔΩ=
∫0
L
dz∫ΔΩ
dΩ[(d σdΩ
)Ros
⋅ϵ⋅APV ]
∫0
L
dz∫ΔΩ
dΩ[(d σdΩ
)Ros
⋅ϵ ]
de
tect
ion
yie
ld/p
.e.
de
tect
ion
yie
ld/p
.e.
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What is the number of detected e-p events?
To determine Δsin2(θW), we sample the mapping:
with
Δ Aexp≈1 /√N and : Total number of detected e-p eventsN
N=Φ⋅ρ⋅T⋅⟨d σdΩ
⟩L,Δ Ω
⋅Δ Leff⋅ΔΩeff
Δ L eff⋅ΔΩeff=∫0
L
dz∫ΔΩ
d Ω[ y (z ,θ)]
⟨dσdΩ
⟩L ,ΔΩ
=
∫0
L
dz∫ΔΩ
dΩ[(d σ
dΩ)Ros
⋅ϵ]
∫0
L
dz∫ΔΩ
dΩ[ϵ]
with ,
y( z , θ) : Detection efficiency distributionProbability for an elastic e-p event with (z, θ) to produce a signal in the virtual detector
sin2(θW)=Ζ( Aexp , Aapp ,E ,P ,L ,ΔΩ ,Re(□γ Z ) ,{f i})
de
tect
ion
effi
cie
ncy
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Prototype tests @ MAMI
Quartz
Lightguide
θ scan data:
PMT
θ
e-
Measured the yield of photo electrons for different
● materials(quartzes, wrappings, lightguids, PMTs)
● geometries
● impact positions
● angles of incidence
ADC channel
coun
ts
(K. Gerz & D. Rodriguez)
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APV is dominated by QW(p) at low values of Q2.
Gorchtein, Horowitz, Ramsey-Musolf 1102.3910 [nucl-th]
Low Q²?
At low beam energies: Uncertainty of γ-Z-box contribution to sin2(θW) is negligible.
Q2=4EE ' sin2 lab /2
Low Q²: Low beam energy and large angle or vice versa?
γ-Z-box correction to QW(p)